folding · Paper Toy

Six-fold, flat-fold, Paper-fold

Paper Folding the Ferozkah Jaali
Paper Folding the Ferozkah Jaali

I found a fold.

If paperfolding graps your attention, prepare to be overwhelmed.  There’s three things to unpack here: the fold, the pattern on the fold, and how they interact.

I had been wondering if I could fold a tetrahedron out of a rectangle.

Tetrahedrons and other shapes
tetrahedrons and other shapes

Turns out, yes. I can make a tetrahedron with a square base or a triangular base out of the same piece of paper using the same folds in different ways.

Looks like a fish
Looks like a fish

Then I started seeing that I could make other shapes out of the same pieces of paper using the same folds differently.

Some shapes are flat, others are dimensional.

I’ve been playing with these all week, and I am still finding different shapes that these folds create.

 

I’ve also been drawing this six-fold pattern from Islamic Geometry called the Ferozkoh Jaali. It occurred to me that it would go perfectly with the folds I was making.

detail of Ferozkah Jaali
detail of Ferozkah Jaali

 

This is just a small portion of the pattern. I’ve been coloringing copies of these in all week, trying to get to know the shapes.

Here’s the fold that I’m using:

 

Mountain and Valley folds
Mountain and Valley folds

It’s four mountain folds (diagonals) and two valley folds (horizontal and vertical) that are created around equilateral triangles. Oh, and there’s a slice in the middle. One horizontal slice.

Now here’s the first wonderful thing about using this image with my folds:

No matter how you use the creases (which are around the equilateral triangles) , the pattern lines up. In the photo above, a corner is peeking through that slice in the paper, and, look, the pattern lines up.

Equilateral triangle(s)
Equilateral triangle(s)

I printed the design on the fronts and backs of my papers, and look, when the paper wraps around itself, the pattern lines up.

Now there is one more thing to mention. Hold on to your seats. This is wonderful. But, first, here’s the foundation of the image I created, first by hand, then on the computer, because I needed the precision of the computer image.

Six-fold-geometry
Six-fold-geometry

Okay, so as I’ve been folding and refolding and refolding again, and finding different shapes all the time, the last final amazing thing that I noticed (and this makes so much sense) ….

Some heart shapes?
Some heart shapes?

…is that every shape I make with these folds can is echoed somewhere in the lines of the  geometric drawing that is printed on the paper.

This makes me so happy, well, I can’t even describe it.

Another heart shape
Another heart shape

Well, there you have it. Hope you love it as much as I do.

covered with NOT geometry
covered with NOT geometry

Oh, and just in case you’re wondering, I think this fold looks good with just about anything on it.

Am seriously considering making a bunch of these and offering them for sale, probably through Etsy. Stay tuned….

 

 

 

Art and Math · folding · geometry and paperfolding · Math and Paper Folding

Constructing a Shape then Admiring It

Paper folding in the morning
Paper folding in the morning

Yesterday I watched a video that showed the Lawler family looking at shapes.

https://mikesmathpage.wordpress.com/2017/01/13/exploring-3-intersecting-cylinders-with-3d-printing/
https://mikesmathpage.wordpress.com/2017/01/13/exploring-3-intersecting-cylinders-with-3d-printing/

One of Mike’s sons said he liked the top shape in the image above. You can’t see from the photo, but it’s a full sphere. The image above is only half of the sphere, the other half looks no different than the half that is showing. I’ve played around with constructing foldable versions of shapes that look something like the one above, and I thought I’d be able to make a foldable version of what was on Mike’s screen.

Template for folding and cutting
Template for folding and cutting

I’m not showing all the steps that led to this map of folding and cutting because what I’m most interested in showing here are the wonderful visuals I got to experience along the way of creating the final structure.

Folding and Cuttin
Folding and Cutting

Silly as it may seem, one of my first realizations was that the indoor, nighttime lighting in my workspace was just all wrong for photographing what I was about to fold. Morning light would be best. So I went to bed.

Assembling in the morning light
Assembling in the morning light

Of course I forgot to recharge the battery of my phone camera before I went to bed, so I didn’t get the earliest light.

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Hmm, I don’t really want to say much more about this process. I’m just going to post pictures now. (Haven’t had my coffee yet.)

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wp-1484487640608.jpg

img_20170115_082242.jpg

img_20170115_082605.jpg

zzzz

Ok. Time for coffee. Am heading to Rochester today to bring my daughter back to college. Will be thinking about all shapes that this structure made. (Which reminds me of a question someone once asked me, “What, do you just sit around thinking about folding paper?” Well, yeah.)

folding · How-to

Synchronizing the Folded Line

black and red Pockets Folder by Paula Beardell Krieg
Perfectly Folded Pockets

This is a reference, nuts-and-bolts kind of post about how to create an even fold across the length of a piece of paper. This is a detail of paper-folding and bookmaking that is so valuable that it deserves to be looked at all by itself. I’m not going to explain how to make the accordion folds for the book above, but between this post and my accordion book tutorial page, you can put the info together and make something like what I’ve pictured. Now, on to folding up edges!

Pockets Folder in progress w
This is the look that I’m going after: the bottom edge of the paper has been evenly folded up to create a Pocketed Book

The paper in the above photo is 24 inches (61 cm) long and it was 10 inches (26 cm) high before I folded up a 3 inches (8 cm) flap to create a pocketed book. There is a specific, absolutely-essential-to-know, bordering-on-magic, completely-impressive, impossible-for-bookmakers-and-paperfolders-to-live-without-knowing technique that makes this seemingly impossible fold possible and easy to accomplish.

pockets folder first fold w

 

Here’s what to do to make sure that you fold the paper evenly across the length of the page.

  • Start in the middle of the paper
  • Focus on the folded line
  • Curl the paper up making sure the folded lines are lined up with each other exactly
  • Make sure that the folded lines are lined up with each other exactly (yes, I know I just said that, but it’s worth saying again)
  • Holding the paper so that the folded lines exactly line up, slowly slide your fingers across the curl of the paper to create a crease

pockets folder sliding down

  • As you approach the next set of folded lines, make sure that these lines are lined up with each other exactly.
  • Holding the paper so that the folded lines are lined up exactly, slide your fingers across the curl of the paper to create a crease.

pockets folderfinal slide w

 

 

  • As you approach the next set of folded lines (which, in the case of the photo above, is the last set of folded lines) make sure that these lines are lined up with each other exactly.
  • Finish off the fold, then return to the center of the paper and repeat going in the opposite direction.

Pockets Folder in progress w

 

And there you have it, again, a perfectly even fold across the length of the paper!